Find the shortest distance from the point P = (2,2,5)
2,712
Hint: Let $u=\langle 2,2,5\rangle$ and $v=\langle 6,5,4\rangle$, and find $\displaystyle d=\frac{|u\times v|}{|v|}$.
Related videos on Youtube
12 : 51
How to find the shortest distance from a point to a line - Vectors in 3D
12 : 00
How to find Minimum Distance from a point to the Curve Application Derivatives MCV Calculus
08 : 23
Shortest distance of a point to a line : ExamSolutions Maths Revision
10 : 11
Two methods to find shortest distance of a point from Plane
16 : 47
§3.6 Optimization: Minimum Distance from a Point to a Curve
Author by
Yusha
Updated on August 15, 2022Comments
-
Yusha 9 months
Find the shortest distance from the point $P = (2,2,5)$ to a point on the line given by $l:(x,y,z) = (-6t, -5t, -4t)$
So I've got the matrix that I think it should look like which is
$\begin{bmatrix}-6&-5&-4\\2&2&5\end{bmatrix}$ but what exactly am I solving here
-
Yusha almost 7 yearsThe derivative of $d(t) = 0$
-
Kaj Hansen almost 7 yearsI'm recommending minimizing $f(t) = (d(t))^2$ by first finding $\displaystyle \frac{df}{dt}$. -
Yusha almost 7 yearsthere is no $f$
-
Kaj Hansen almost 7 yearsI'm just defining it to be the function $(d(t))^2$ for notational convenience.
-
Yusha almost 7 yearsThis is not a calculus class, this is linear algebra. Shouldn't have to use any sort of calculus for this
-
Kaj Hansen almost 7 yearsThat's alright; you don't have to accept my answer, and we can wait on someone else. I believe in having diverse solutions posted nevertheless.